Unit 8: Circle Geometry Grade 9 Math Introduction ...

Unit 8: Circle Geometry

Introduction: Definitions

Grade 9 Math

Diameter

the distance across a circle, measured through its

center; or the line segment that joins two points on

the circle and passes through the center.

Radius

the distance or line segment from the center of a

circle to any point on the circle.

Chord(s)

a line segment that joins two points on a circle.

A

Arc

B

A segment of the circumference of a circle.

Minor Arc

The shorter of two arcs between two points on a circle.

For example: AB

Tangent

a line that intersects a circle at only one point.

Point of Tangency

the point where a tangent intersects a circle

Central Angle

An angle whose arms are radii of a circle.

Q

Inscribed Angle

An angle in a circle with its vertex and endpoints

of its arms on the circle.

P

R

For example,

PQR

Section 8.1 Properties of Tangents to a Circle

Tangent-Radius Property

A tangent to a circle is perpendicular to the radius

at the point of tangency.

APO = BPO = 900

Example Problems

A)

Point O is the center of a circle and AB is tangent to the circle. In

AOB = 550. Determine the measure of OBA.

Since

A = 900 and

OAB,

0 = 550

Then 90 + 55 = 145

The three angles in a triangle

add to 1800. So

145 = 350.

x = 180 ¨C

Try to find the missing angles in the following diagrams

A)

B)

x = 48o

x = 76o

Application Example

Since AC is a tangent ¡­

BDA = BDC = 900

Find x

x + 90 + 57 = 180

x + 147 = 180

x + 147 - 147 = 180 - 147

x = 33o

Find y

y + 90 + 35 = 180

y + 125 = 180

y + 125 - 125 = 180 - 125

y = 55o

Using the Pythagorean Theorem in a Circle

1.

Since BM is a tangent we know

that OBM = 900.

a 2 + b 2 = c2

82 + b2 = 102

64 + b2 = 100

b2 = 100 ¨C 64

b2 = 36

b= ¡Ì36

b = 6 cm

Try this one!

2.

Since BM is a tangent we know

that OBM = 900.

a 2 + b 2 = c2

122 + b2 = 162

144 + b2 = 256

b2 = 256 ¨C 144

b2 = 112

b= ¡Ì112

b = 10.6 cm

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